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On an Extension Problem for Polynomials
Author(s) -
Bakonyi Mihály,
Timotin Dan
Publication year - 2001
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609301008268
Subject(s) - mathematics , uniqueness , extension (predicate logic) , norm (philosophy) , operator (biology) , fourier transform , function (biology) , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , law , gene , programming language , biochemistry , chemistry , repressor , evolutionary biology , biology , computer science , political science , transcription factor
Consider the following problem: given complex numbers a 1 , …, a n , find an L ∞ function f of minimum norm whose Fourier coefficients c k ( f ) are equal to a k for k between 0 and n . We show the uniqueness of this function, and we estimate its norm. The operator‐valued case is also discussed. 2000 Mathematics Subject Classification 30E05, 47A20, 47A56, 47A57.